1. An Uncooperative Universe: large scale anomalies in the CMB
Glenn Starkman
Institute for the Science of Origins
CERCA, and Department of Physics
Case Western Reserve University
Cosmology on Safari 2017
Let your model guide you, but you can’t let your model boss you around.
Don’t just ask the questions your model tells you are interesting, b/c you
might get interesting answers to uninteresting questions. That is what forces you to think harder about your model.
Craig Copi, Dragan Huterer
& Dominik Schwarz
Francesc Ferrer, Amanda Yoho
S. Aiola, A. Kosowsky
L. Knox, Marcio O’Dwyer; \
“photo”: ESA/ Planck
Image: NASA/WMAP

2. WMAP NASA/WMAP Science team
Galactic foreground removed by taking linear combination of bands.
NASA/WMAP Science team

3. Planck NASA/WMAP Science team
Galactic foreground removed by taking linear combination of 5 bands.
NASA/WMAP Science team

4. Angular Power Spectrum
Cl = (2l +1)-1m |al m|2
T = l mal m Yl m(,)
Standard model for the origin of fluctuations (inflation):
al m are independent (nearly?) Gaussian random variables, with < al m a*l’ m’> = Cl l l ‘mm’
Sky is statistically isotropic and Gaussian random,
(almost) ALL interesting information is contained in Cl

5. Angular Power Spectrum
NASA/WMAP Science team
Cl = (2l +1)-1m |al m|2
T = l mal m Yl m(,)
6 parameter fit to >>6 points
Planck 2013 Paper I.

6. Great experimental accomplishment
Remarkable agreement with theory, especially for the statistics that the theory prefers
BUT ! or but?
Not talk about: cold spot (yesterday), SH (not anomalous), …

7. Is there anything interesting left to learn about the Universe on large scales?

8. Outline Alignments at low-l : The low-l / large-angle problem:
The failure of statistical isotropy.
The low-l / large-angle problem:
The vanishing of C()
And hemispheres, parity, first peak (, …?)
Not talk about: cold spot (yesterday), SH (not anomalous), …
Troubles in cosmological paradise?
Can we tell? Even without a model?

9. “The Low-l Anomaly”
Original Motivation:

10. Beyond Cl: Searches for Departures from Gaussianity/Statistical Isotropy
angular momentum dispersion axes (da Oliveira-Costa, et al.)
Genus curves (Park)
Spherical Mexican-hat wavelets (Vielva et al.)
Bispectrum (Souradeep et al.)
North-South asymmetries (Eriksen et al., Hansen et al.)
dipolar modulations
Cold hot spots, hot cold spots (Larson and Wandelt)
Land & Magueijo scalars/vectors
even/odd Cl anomaly
your favourite technique/anomaly that I missed
multipole vectors
(Copi, Huterer & GDS; Schwarz, SCH; CHSS;
also Weeks; Seljak and Slosar; Dennis)

11. Alignments …

12. Multipole Vectors Advantages: 1) û (1,1) is a vector, A(1) is a scalar
Q: What are the directions associated
with the l th multipole:
Tl ()  m al mYl m () 
Dipole (l =1) :
m a1mY1m () =
A(1) (ûx(1,1), ûy(1,1), ûz(1,1)) (sin cos, sin sin, cos)
Advantages: 1) û (1,1) is a vector, A(1) is a scalar
2) Only A(1) depends on C1

13. Multipole Vectors {{al m, m=- l,…, l }, l =(0,1,)2,…} 
General l, write:
m al mYl m () 
A (l) (û (l,1)ê)…(û (l, l) ê )
- all traces]
{{al m, m=- l,…, l }, l =(0,1,)2,…} 
{A(l) ,{û (l,i),i =1,… l }, l = (0,1,)2,…}
Advantages: 1) û(l,i) are vectors, A(l) is a scalar
2) Only A(l) depends on Cl

14. Maxwell Multipole Vectors
m al mYl m ()  A(l) (û (l,1))… (û (l,l) )r -1] r=1
manifestly symmetric AND trace free:
2 (1/r)  (r)
J.C. Maxwell, A Treatise on Electricity and Magnetism, v.1, 1873 (1st ed.)

15. Area Vectors Notice: Suggests defining:
Quadrupole has 2 vectors, i.e. quadrupole is a plane
Octopole has 3 vectors, i.e. octopole is 3 planes
Suggests defining:
w(l,i,j)  (û (l,i) x û (l,j)) “area vectors”
Carry some, but not all, of the information
Relation to ni:
w(2,2,2) || n2
octopole is perfectly planar if w(3,1,2) || w(3,2,3) || w(3,3,1)
and then: n3 || w(3,I,j)
A. de Oliveira-Costa, M. Tegmark, M. Zaldarriaga, A. Hamilton. Phys.Rev.D69:063516,2004

16. l=2&3 Area Vectors ecliptic SGP l=3 normal l=3 normal equinox
dipole
l=3 normal
ecliptic
Quadrupole–octopole axis IS the “Axis of Evil” of Land and Maguejio
SGP

17. Quadrupole plane & 3 octopole planes are:
aligned
perpendicular to the ecliptic
normal to the dipole

18. Area vectors tell about the orientations
of the multipole planes.
Can still rotate the aligned planes
about their common axis.

19. l=2&3 : The Map
Note: ecliptic, N-S asymmetry

20. (WMAP3) Alignment “probabilities”
p-value of the quadrupole & octopole planes being so aligned:
( )%
Conditional p-value of these planes being so perpendicular to the ecliptic (solar system):
( )%
Conditional p-value of aligned planes perpendicular to the ecliptic pointing at the dipole/equinox:
few%
Conditional p-value of aligned planes perpendicular to the ecliptic pointing at the dipole/equinox, rotated to have ecliptic separate high and low variance hemispheres:
WMAP 3
few%
Net : < 10-7

21. Planck vs. WMAP MPV Important to remove Doppler quadrupole
As Martin Quantin reminded us …Important to remove Doppler quadrupole
Important to remove Doppler quadrupole

22. Planck vs. WMAP MPV

23. Quadrupole+Octopole Correlations
Cosmology (“Physical Model”)
but how to get dipole correlation?
how to get C2 < C3 ?
Systematics
how do you get such effects?
esp., how do you get a N-S ecliptic asymmetry? (dipole mis-subtraction?)
how do you avoid oscillations in the time-ordered data?
how do you get the systematics in both WMAP and Planck
The Galaxy: (Systematics/Physical Model)
has the wrong multipole structure (shape)
is likely to lead to GALACTIC not ECLIPTIC/DIPOLE/EQUINOX correlations
Other Foregrounds -- difficult:
Changing a patch of the sky typically gives you: Yl0
Sky has 5x more octopole than quadrupole
How do you get a physical ring perpendicular to the ecliptic
Caution: can add essentially arbitrary dipole, which can entirely distort the ring! (Silk & Inoue)
How do you hide the foreground from detection? T≈TCMB

24. Conclusions? How to make progress? Alignments are: Persistent
Individually interesting, collectively significant
but hard to explain, or establish “priority”
How to make progress?

25. The uncorrelation …

26. “The Low-l Anomaly”
The low
quadrupole

27. “The Large-Angle Anomaly”

28. Angular Correlation Function C()
C() = < T(T)>cos
But C() = l Cl Pl(cos ())
 Same information as Cl, just differently organized
Why should C() be interesting?

30. Two point angular correlation function -- WMAP3

31. The Large-Angle Anomaly: Is it Significant?
One measure (WMAP1):
S1/2 = -11/2 [C()]2 d cos 

32. Statistics of C(θ)

33. Origin of C(θ)

34. Only 5% of LCDM realizations have low a full-sky S1/2
Is it an accident?
Only 5% of LCDM realizations have low a full-sky S1/2
Only 2% of rotated and cut full skies with such low full-sky S1/2, have this low a cut-sky S1/2

35. Statistics of C(θ)
% of realizations of the concordance model of inflationary ΛCDM have so little cut sky large-angle correlation !
Either: this reflects a <0.1% probable full sky C(θ), or a 5% probable C(θ) and a 2% probably alignment with the galaxy

36. Did this change in Planck?

37. CR minimal mask
Kq75y9 mask

38. Planck R1 Copi, Huterer, Schwarz, GDS arxiv 1310.3831 MNRAS (in press)
Full sky expected 50,000
Copi, Huterer, Schwarz, GDS arxiv MNRAS (in press)

39. S1/2 vs. Cl S1/2 is NOT small (just) because C2 is small,
nor because Cl are small
but because C2, C3, C4, C5 cancel C6,…
“The steep, nearly linear rise in the spectrum from l = 2 to 5 translates to a near absence of power in the angular correlation function at separations larger than ~6[0]° (Spergel et al. 2003; Bennett et al. 2003b). This was also seen in the COBE DMR data, but it is now clear that this is not due to Galaxy modeling errors.” WMAP team – Yr 1
Figure 1. Two-point angular correlation function from the inpainted Planck SMICA map. The black, dotted line shows the best-fitting ΛCDM model from Planck. The shaded, cyan region is the 68 per cent cosmic variance confidence interval. Included from the SMICA map are the C(θ) calculated on the full-sky (black, solid line) and from two cut skies using the U74 mask (green, dash-dotted line) and the KQ75y9 mask (red, dashed line). See the text for details.

40. Violation of GRSI
Even if we replaced all the theoretical Cl by their measured values up to l=20, cosmic variance would give only a 3% chance of recovering this low an S1/2 in a particular realization
and most of those are much poorer fits to the theory than is the current data

41. Explanations This is a statistical fluke in standard LCDM
It’s physics!
Possible physics implications:
R(r)Ylm(Ω) are wrong basis to preserve Gaussianity
Examples:
a) cosmic topology (=> eigenmode basis)
b) ξ(|x1-x2|>R)=0 (=> compact support basis)

42. Low Northern Variance Power asymmetry Dipole modulation
Compare S vs N. North looks much “quieter”
Low Northern Variance

43. Expanded/confirmed/… by many:
“Eriksen et al. (2004) and Hansen et al. (2004) … discovered that the angular power spectrum of …WMAP[1] data, when estimated locally at different positions on the sphere, appears not to be isotropic.”
Planck 2013 XXIII.
Expanded/confirmed/… by many:

44. Compare S vs N. North looks much “quieter”

45. SMICA N vs S variance
Temperature variance distributions for the unconditioned-CDM realizations considering two dffierent sky coverage scenarios:
pixels in the northern Ecliptic hemisphere (Ecliptic-North, left), southern Ecliptic hemisphere (Ecliptic-South, middle) and the portion of
the northern Ecliptic hemisphere that can be seen from the Chilean Atacama site (Atacama-North, right). The vertical lines represent the
corresponding values calculated from the Planck SMICA temperature map with p-values displayed in the plot legends. The Ecliptic-North
temperature data has an anomalously low variance (p = 0:1 per cent) when compared with unconditioned-CDM while the Ecliptic-
South appears unremarkable (p = 42:3 per cent). The north variance p-value increases to 1:0 per cent when only the Atacama-North
pixels are considered. See section 2.2 for parameters.
p ~ 0.001

46. And …
A couple of more
that I find intriguing

47. Advances in Astronomy, vol. 2012, id. 960509

48. Angular Power Spectrum
At least 3 other major deviations in the Cl in 1st year data

49. Power spectrum: ecliptic plane vs. poles
“First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations:
The Angular Power Spectrum”
G. Hinshaw, et.al., 2003, ApJS, 148,
only v.1 on archive
NOTE: S/N of these (especially at peak) are not high.
All 3 other major deviations are in the ecliptic polar Cl only!!

50. With so many anomalies, what do we do?
Compare S vs N. North looks much “quieter”

51. Making Progress
Find a fundamental physics model, make testable predictions & test them.
Make predictions from reasonable phenomenological extrapolations & test them.
Adopt the “fluke hypothesis,” use it to make predictions & test them.

52. New Models
List of of new fundamental physics models that explain (multiple) anomalies:

53. Phenomenological extrapolations
Philosophy: assume each anomaly is “real” and guess what that implies for other observables

54. Testing the fluke hypothesis
Philosophy: assume LCDM is correct, and see how the measured anomalies affect predictions for other observables.
Figure1.Histogram of ST'1=2 values for 105 simulations for con-strained (blacksolid) and unconstrained (reddashed)CDM realizations from WMAP7 parameters.The dashed lines show the 99- percentile and 99:9- percentile values for the constrained realizations.

55. Constrained realizations (testing the fluke hypothesis)
Create realizations of (best-fit) ΛCDM
Constrained to agree with observed T anomalies
Better: constrained to agree with observed maps.
Figure1.Histogram of ST'1=2 values for 105 simulations for con-strained (blacksolid) and unconstrained (reddashed)CDM realizations from WMAP7 parameters.The dashed lines show the 99- percentile and 99:9- percentile values for the constrained realizations.
Augment with realizations of other physical quantities with correct covariance (eg. polarization, lensing potential)

56. Testing the fluke hypothesis+
Figure1.Histogram of ST'1=2 values for 105 simulations for con-strained (blacksolid) and unconstrained (reddashed)CDM realizations from WMAP7 parameters.The dashed lines show the 99- percentile and 99:9- percentile values for the constrained realizations.
Phenomenological extrapolations

57. Low northern variance

58. Phenomenological guess
Low variance in T over a large region of the sky should imply low variance in polarization (at least E-mode) in that same region

59. After all, T-E are correlated!
What does LCDM say?
After all, T-E are correlated!
Solid: LCDM
LCDM conditioned on SMICA map.

60. a small reduction in the polarization variance
Solid: LCDM
LCDM conditioned on SMICA map.
Observe:
a small reduction in the polarization variance
approximately equal in N and S

61. Test of the phenomenological guess
Recall: T variance was 10% supressed!
Look for reduced variance in North Ecliptic E
10% variance suppression => extremely low p-value

62. Example 2: Absence of two-point angular correlation
Figure1.Histogram of ST'1=2 values for 105 simulations for con-strained (blacksolid) and unconstrained (reddashed)CDM realizations from WMAP7 parameters.The dashed lines show the 99- percentile and 99:9- percentile values for the constrained realizations.

64. Phenomenological guess
Absence of angular correlation in T implies absence of angular correlation in polarization (at least E, and so Q and U Stokes parameters)

65. What does LCDM say?
If CTT(θ>60)~0 is a fluke, other correlation functions are affected (Dvorkin, Peiris & Hu 2008)
Solid: LCDM
LCDM conditioned on SMICA map.

66. Predicted TQ correlations
CTQ(θ>60)~0 is affected
Figure1.Histogram of ST(23-174) values for 105 simulations for con-strained (blacksolid) and unconstrained (reddashed)CDM realizations from WMAP7 parameters.The dashed lines show the 99- percentile and 99:9- percentile values for the constrained realizations.
but signficant correlation is still “expected”

67. Constrained-LCDM QQ and UU correlations
A. Yoho, A. Aiola, C. Copi, A. Kosowsky, GDS (PRD91 (2015) 12, )
Implication – if the absence of TT correlations at large angles is due to an absence of \Phi\Phi correlations at large distances, then this should result in an absence of QQ/UU correlations

68. Predicted (local)E/B-mode correlations
Implication – if the absence of TT correlations at large angles is due to an absence of \Phi\Phi correlations at large distances, then this should result in an absence of QQ/UU correlations
Phenomenological guess of suppressed S1/2QQ or S1/2UU would be unlikely in LCDM if low enough. (Suppression of <1/20 in TT.)

69. Phenomenological guess
Absence of angular correlation is due to absence of spatial correlation in 3d
Consequence: expect low/no correlation in:
(T, E, B?, φ, δ(z), …) x (T, E, B?, φ, δ(z’), …)

70. Eg. T-lensing correlations
Figure1.Histogram of ST'1=2 values for 105 simulations for con-strained (blacksolid) and unconstrained (reddashed)CDM realizations from WMAP7 parameters.The dashed lines show the 99- percentile and 99:9- percentile values for the constrained realizations.
LCDM predicts mild suppression of Tφ

71. Another phenomenological prediction --
the cosmological dipole
C(θ) has had the monopole and dipole subtracted.
If C(θ>60)~0 is physical, then the cosmological dipole must be small
C1 < ~ 200 (μK) (C1th ~ 3300(μK)2 )
Q: can you detect the/this dipole?

72. SUMMARY
The (low-l) sky appears NOT to be a realization of a Gaussian random statistically isotropic field.

73. SUMMARY The T sky lacks large-angle correlations
Temperature multipoles are aligned with one another and/or with the ecliptic/dipole
The T sky lacks large-angle correlations
There are noticeable hemispherical asymmetries/differences
etcetera

74. No good “model” so far:
Systematics
Foregrounds
Cosmology

75. They’re trying very hard to hush it up.
While the cosmic orchestra may be playing the LCDM symphony, somebody gave the bass and tuba the wrong score.
They’re trying very hard to hush it up.
There is no good theory for any of this, yet!
But we may be able to test explanations anyway.